Moran Sets and Hyperbolic Boundaries

In the paper, we prove that a Moran set is homeomorphic to the hyperbolic boundary of the representing symbolic space in the sense of Gromov, which generalizes the results of Lau and Wang [Indiana U. Math. J. {\bf 58} (2009), 1777-1795]. Moreover, by making use of this, we establish the Lipschitz equivalence of a class of Moran sets.Comment: 14 pages, 1 figur

Comment on "General nonlocality in quantum fields"

In this paper, we first incorporate the weak interaction into the theory of General Nonlocality by finding a appropriate metric for it. Accordingly, we suggest the theoretical frame of General Nonlocality as the candidate theory of unifying three microscope interactions in low energy limit. In this unifying scenario, the essential role of photon field is stressed.Comment: Only partial content published in the following reference. The part asserting the fermion mass problem now proved to be wrong, though remains in the versio

Rauzy fractals with countable fundamental group

We prove that every free group of finite rank can be realized as the fundamental group of a planar Rauzy fractal associated with a 4-letter unimodular cubic Pisot substitution. This characterizes all countable fundamental groups for planar Rauzy fractals. We give an explicit construction relying on two operations on substitutions: symbolic splittings and conjugations by free group automorphisms.Comment: 14 pages, v3 includes some corrections to match the published versio

Energy Efficient Downlink Transmission for Multi-cell Massive DAS with Pilot Contamination

In this paper, we study the energy efficiency (EE) of a downlink multi-cell massive distributed antenna system (DAS) in the presence of pilot contamination (PC), where the antennas are clustered on the remote radio heads (RRHs). We employ a practical power consumption model by considering the transmit power, the circuit power, and the backhaul power, in contrast to most of the existing works which focus on co-located antenna systems (CAS) where the backhaul power is negligible. For a given average user rate, we consider the problem of maximizing the EE with respect to the number of each RRH antennas $n$, the number of RRHs $M$, the number of users $K$, and study the impact of system parameters on the optimal $n$, $M$ and $K$. Specifically, by applying random matrix theory, we derive the closed-form expressions of the optimal $n$, and find the solution of the optimal $M$ and $K$, under a simplified channel model with maximum ratio transmission. From the results, we find that to achieve the optimal EE, a large number of antennas is needed for a given user rate and PC. As the number of users increases, EE can be improved further by having more RRHs and antennas. Moreover, if the backhauling power is not large, massive DAS can be more energy efficient than massive CAS. These insights provide a useful guide to practical deployment of massive DAS.Comment: 12 pages,10 figures. Accepted by the IEEE Transactions on Vehicular Technolog